1. **State the problem:** Simplify the expression $$(4s-4)(-s^2 + 3s + 1)$$. 2. **Recall the distributive property:** To multiply two polynomials, multiply each term in the first polynomial by each term in the second polynomial. 3. **Factor out common terms if possible:** Notice $4s - 4 = 4(s - 1)$, which might simplify multiplication. 4. **Multiply:** $$4(s - 1)(-s^2 + 3s + 1) = 4 \times (s - 1) \times (-s^2 + 3s + 1)$$ 5. **First multiply $(s - 1)$ and $(-s^2 + 3s + 1)$:** $$s \times (-s^2 + 3s + 1) = -s^3 + 3s^2 + s$$ $$-1 \times (-s^2 + 3s + 1) = s^2 - 3s - 1$$ 6. **Add the results:** $$(-s^3 + 3s^2 + s) + (s^2 - 3s - 1) = -s^3 + 4s^2 - 2s - 1$$ 7. **Multiply by 4:** $$4 \times (-s^3 + 4s^2 - 2s - 1) = -4s^3 + 16s^2 - 8s - 4$$ **Final answer:** $$-4s^3 + 16s^2 - 8s - 4$$